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International Journal of Modern Physics B

VORTEX LATTICE STATE OF A SUPERFLUID FERMI GAS IN THE UNITARY REGION

Meng Gao, Lan Yin

Published Sep 20, 2008• 3 citations

Abstract

In this paper, we study the structure of vortex lattices in a trapped superfluid Fermi gas in the unitary region near the superfluid transition temperature. A phenomenological approach based on the Ginzburg-Landau theory is used. Two types of stable triangular vortex lattices are found numerically at the same rotation frequency. In type (A), the trap center is occupied by a vortex; in type (B), there are three vortices closest to the trap center which is unoccupied. The lattice structures at different rotation frequencies and temperatures are analyzed. The vortex density increases linearly with the rotation frequency, very close to the analytical estimation. The superfluid and type-(B) vortex lattice do not disappear together. At high rotation frequencies, the vortex lattice disappears, but there exists a localized superfluid state near the trap center. The superfluid vanishes at a critical rotation frequency consistent with the theory for the upper critical magnetic field of type-II superconductors.

DOI: 10.1142/s0217979208048814

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In this paper, we study the structure of vortex lattices in a trapped superfluid Fermi gas in the unitary region near the superfluid transition temperature. A phenomenological approach based on the Ginzburg-Landau theory is used. Two types of stable triangular vortex lattices are found numerically at the same rotation frequency. In type (A), the trap center is occupied by a vortex; in type (B), there are three vortices closest to the trap center which is unoccupied. The lattice structures at different rotation frequencies and temperatures are analyzed. The vortex density increases linearly with the rotation frequency, very close to the analytical estimation. The superfluid and type-(B) vortex lattice do not disappear together. At high rotation frequencies, the vortex lattice disappears, but there exists a localized superfluid state near the trap center. The superfluid vanishes at a critical rotation frequency consistent with the theory for the upper critical magnetic field of type-II superconductors.

The behavior of a dilute two-component neutral superfluid Fermi gas subjected to rotation is investigated within the context of a weak-coupling BCS theory. The microscopic properties at finite temperature are obtained by iterating the Bogoliubov-de Gennes equations to self-consistency. In the model, alkali atoms are strongly confined in quasi-two-dimensional traps produced by a deep one-dimensional optical lattice. The lattice depth significantly enhances the critical transition temperature and the critical rotation frequency at which the superfluidity ceases. As the rotation frequency increases, the triangular vortex arrays become increasingly irregular, indicating a quantum melting transition.

We consider a superfluid of trapped fermionic atoms and study the single vortex solution in the Ginzburg-Landau regime. We define simple analytical estimates for the main characteristics of the system, such as the vortex core size, temperature regimes for the existence of a vortex, and the effects of rotation and interactions with normal fermions. The parameter dependence of the vortex core size (healing length) is found to be essentially different from that of the healing length in metallic superconductors or in trapped atomic Bose-Einstein condensation in the Thomas-Fermi limit. This is an indication of the importance of the confining geometry for the properties of fermionic superfluids.

We study a superfluid in a rotating anharmonic trap and explicate a rigorous proof of a transition from a vortex lattice to a giant vortex state as the rotation is increased beyond a limiting speed determined by the interaction strength. The transition is characterized by the disappearance of the vortices from the annulus where the bulk of the superfluid is concentrated due to centrifugal forces while a macroscopic phase circulation remains. The analysis is carried out within two-dimensional Gross-Pitaevskii theory at large coupling constant and reveals significant differences between ``soft'' anharmonic traps (like a quartic plus quadratic trapping potential) and traps with a fixed boundary: in the latter case the transition takes place in a parameter regime where the size of vortices is very small relative to the width of the annulus, whereas in soft traps the vortex lattice persists until the width of the annulus becomes comparable to the vortex cores. Moreover, the density profile in the annulus where the bulk is concentrated is, in the soft case, approximately Gaussian with long tails and not of the Thomas-Fermi type like in a trap with a fixed boundary.

The stability conditions for the singular vortex which accompanies Majorana zero modes at the core are investigated for p-wave resonant superfluids of atomic Fermi gases. Within the Ginzburg-Landau framework we determine the stable conditions in the parameter space for the external rotation frequency and the harmonic trap frequency. There exists the narrow stable region in this parameter space for quasi-two-dimensional condensates. We also describe the detailed characterizations of the spatial structure of the order parameter in the chiral p-wave superfluids under rotation.

The rotational properties are studied for a unitary superfluid gas of fermions at zero temperature. Using a hydrodynamic approach, the conditions for the formation of a giant vortex are discussed. It is found that in the present approximation, an anharmonic addition to the usual harmonic-oscillator type of trap potential is necessary for the energetic stability of a giant vortex. To determine the conditions quantitatively, a Thomas-Fermi approach is compared with numerical solutions in three dimensions.